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Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
Professional Development Session for Teachers in California by singaporemath.com April 2010
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Professional Development Session for Teachers in California by singaporemath.com April 2010

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William Jackson presented the morning session. Yeap Ban Har presented this in the afternoon.

William Jackson presented the morning session. Yeap Ban Har presented this in the afternoon.

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  • 1. Theoretical Underpinnings of Singapore Math
    Sheraton San Diego Mission Valley Hotel, San Diego CA
    SingaporeMath.com
    Professional Development
    Please download from www.mathz4kidz.com
    Yeap Ban-Har, Ph.D.
    National Institute of Education
    Nanyang Technological University
    Singapore
    banhar.yeap@nie.edu.sg
    DaQiao Primary School
  • 2. Catholic High School (Primary)
  • 3. video of dice problem
    solving problems
    instructional models
    overview
    Bruner’s theory
    Skemp’s theory
    Dienes’ theory
  • 4. introduction
    Wellington Primary School
  • 5. Task
    Lesson Study Problem
    Wellington Primary School
    Move 3 sticks to make 3 squares.
  • 6. Task
    Move 3 sticks to make 3 squares.
  • 7. Task
    Move 3 sticks to make 3 squares.
  • 8. Task
    Move 3 sticks to make 2 squares.
  • 9. Task
    Move 3 sticks to make 2 squares.
  • 10. Task
    Move 3 sticks to make 2 squares.
  • 11. A Problem from Singapore Grade 6 National Test
    Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.
    Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.
    How many sweets did Ken buy?
  • 12. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?
    chocolates
    sweets
    Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.
    12
    Jim
    12
    18
    12
    12
    12
    12
    Ken
    3 parts  12 + 12 + 12 + 12 + 18 = 66
    1 part  22
    Half of the sweets Ken bought = 22 + 12 = 34
    So Ken bought 68 sweets.`
  • 13. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
    How many girls wore swimming goggles on that day?
    A Problem from a Singapore Classroom
    Fairfield Methodist Primary School
  • 14.
    • 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
    How many girls wore swimming goggles on that day?
  • 15. 88
    34
    54
    • 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
    How many girls wore swimming goggles on that day?
  • 16. 34 – 20 = 14
    54 – 34 = 20
    34
    54
  • 17. 3 x 7 = 21
    21 girls wear goggles.
    A Curriculum That Helps Average Students Reach High Achievement
  • 18. TIMSS 2007
    Trends in International Mathematics and Science Studies
    1995
    2003
    2007
    Grade 4
    Advanced
    38
    41
    38
    High
    70
    74
    73
    Intermediate
    89
    92
    91
    Low
    96
    98
    97
    North Vista Primary School
  • 19. TIMSS 2007
    Trends in International Mathematics and Science Studies
    Average
    Indonesia
    Thailand
    Malaysia
    Singapore
    Grade 8
    Advanced
    2
    3
    0
    40
    2
    High
    15
    12
    4
    70
    18
    Intermediate
    46
    44
    14
    88
    50
    Low
    75
    66
    48
    97
    82
    Method Used in Singapore Textbooks
  • 20. Beliefs
    Interest
    Appreciation
    Confidence
    Perseverance
    Monitoring of one’s own thinking
    Self-regulation of learning
    Attitudes
    Metacognition
    Numerical calculation
    Algebraic manipulation
    Spatial visualization
    Data analysis
    Measurement
    Use of mathematical tools
    Estimation
    Mathematical Problem Solving
    Reasoning, communication & connections
    Thinking skills & heuristics
    Application & modelling
    Skills
    Processes
    Concepts
    Numerical
    Algebraic
    Geometrical
    Statistical
    Probabilistic
    Analytical
    Mathematics Curriculum Framework
  • 21. Every Child Counts
  • 22. effective
    mathematics
    teaching
    BinaBangsa School, Indonesia
  • 23. Primary Mathematics 1A
    Pedagogical Principle:
    Bruner
  • 24. Number Bonds
    PCF Kindergarten TelokBlangah
  • 25. Number Bonds
    PCF Kindergarten TelokBlangah
  • 26. Bruner
    The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
    Division
    National Institute of Education
  • 27. Division
    Princess Elizabeth Primary School
  • 28. Catholic High School (Primary)
  • 29. mathz4kidz Learning Centre, Penang, Malaysia
    bruner’s theory
    concrete
    A lesson from Earlybird Kindergarten Mathematics
  • 30. mathz4kidz Learning Centre, Penang, Malaysia
    concrete
    experiences
  • 31. from
    concrete
    to
    pictorial
    mathz4kidz Learning Centre, Penang, Malaysia
  • 32. from
    pictorial
    to
    abstract
    All Kids Are Intelligent Series
  • 33. mathz4kidz Learning Centre, Penang, Malaysia
    symbols
  • 34. using
    concrete
    materials
    Professional Development in AteneoGrade School, Manila, The Philippines
    Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
  • 35. Primary Mathematics (Standards Edition) 2A
    Pictorial Before Abstract
  • 36. bruner
    Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
  • 37. skemp’s
    theory
    conceptual
    understanding
    BinaBangsa School, Semarang, Indonesia
  • 38. Keys Grade School, Manila, The Philippines
  • 39. Keys Grade School, Manila, The Philippines
  • 40. Skemp
    Understanding in mathematics
    relational
    (conceptual)
    instrumental
    (procedural)
    conventional
    Teaching for conceptual understanding is given emphasis in Singapore Math.
    Pedagogical Principle:
    Skemp
    Primary Mathematics Standards Edition Grade 6
  • 41. Fraction Division
    Primary Mathematics Standards Edition Grade 6
  • 42. skemp
    Scarsdale Middle School New York
  • 43. Dienes
    Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.
    Pedagogical Principle:
    Dienes
    Primary Mathematics Standards Edition
    Primary Mathematics Standards Edition Grade 1
  • 44. Pedagogical Principle:
    Dienes
    Primary Mathematics Standards Edition Grade 1
  • 45. Pedagogical Principle:
    Dienes
    Primary Mathematics Standards Edition Grade 2
  • 46. homework
    Are you able to see how these tasks are varied according to Dienes’ idea of mathematical variability?
  • 47. How is Task 4 different from Task 5?
    16
    Primary Mathematics Standards Edition Grade 5
  • 48. 16
    What is the given in Task 5? What is the given in Task 6? Are these different?
    30
    Primary Mathematics Standards Edition Grade 5
  • 49. Earlybird Kindergarten Mathematics
    Standards Edition
    Can you see how Dienes’ idea is used in designing these tasks?
    diene’s
    theory
    of
    variation
  • 50. dienes
    Princess Elizabeth Primary School, Singapore
  • 51. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding
  • 52. conclusion
    PCF Kindergarten PasirRis
  • 53. Instructional Models
    DaQiao Primary School
  • 57. “Children are trulythe future of our nation. “
    Irving Harris
  • 58. This presentation is based on part of one of Singapore pre-service mathematics method courses.
    50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists.
    The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.
  • 59. TEDS-M Elementary Teachers
    Content Knowledge
    TEDS-M Elementary Teachers
    Pedagogical Content Knowledge
  • 60. TEDS-M Middle School Teachers
    Content Knowledge
    TEDS-M Middle School Teachers
    Pedagogical Content Knowledge

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